The Vitruvian Man


L’Uoomo Vitruviano; The Vitruvian Man, is a drawing by the renowned Renaissance polymath Leonardo Da Vinci. Inspired by the work of the ancient Roman architect Vitruvius on the proportions of human anatomy this deceptively simple drawing has deeper and more profound meaning than to just explore the ideal human body proportions.

In the 21st century, the pen and ink drawing is homologous with the picture of perfect health, physique and aesthetic. In the text accompanying the sketch, da Vinci goes on to tediously describe the relationship of proportions in the human body. As an example, an excerpt from the text reads:

“If you open the legs so as to reduce the stature by one-fourteenth and open and raise your arms so that your middle fingers touch the line through the top of the head, knowing that the centre of the extremities of the outspread limbs will be the umbilicus(the navel), and the space between the legs will make and equilateral triangle.”

To understand the significance of the drawing it is first necessary to understand the age old math problem: squaring a circle. How does one take a given area of a circle and make a square with dimensions to equal the area of the circle? The answer? It’s impossible! Simply because of the nature of pi(22/7, 3.142 take your pick).

Leonardo answered this age-old math problem with philosophy. The drawing depicts two men superimposed on another, one in a circle and one in a square. The two sets hands and feet touch the peripheries of the square and the circle.


Shhhhh!! It’s okay, calm down, the answer is at hand!

Vitruvius observed in his original work that the proportion between one’s arm span and height is almost equal. The man with the perpendicularly outstretched arms can, therefore, be said to correspond to a square. Now the same man can “fit” in a circle(as depicted) if one takes the navel as the centre and draws a circle(refer to the excerpt again if this is a little confusing). By taking “man” as the area for both shapes, a philosophical answer was arrived at: that man can fill the area of both shapes.

Is that it? Of course not! The true significance comes from the historical and cultural climate at the time. Neoplatonism was a philosophical movement that outlined the hierarchy of beings in the universe, with God and angels and heaven above, moving down to earth animals and last demons and devils, in a linear chain-like or ladder manner. In its infancy, the belief held that man was in the exact middle of this chain because man consisted of two central identities and traits: a mortal body to show our relationship with all that lies below the centre and will stay on earth, and an immortal soul that will ascend into the heavens.



Giovanni Pico della Mirandola


Now around the time that the Vitruvian Man was born, a Neoplatonist, Giovanni Pico della Mirandola had a different interpretation. He believed that man did not belong at any one fixed point in the chain but rather wherever the individual desired to be and where his actions took him. His understanding was that God had created man to comprehend the beauty and complexity of His universe.

Therefore man was situated at the center but had the unique ability to “change” his position, giving into more basic and primal desires to move down the chain and act like an animal or man could choose to rise and become enlightened in search of knowledge, truth and justice, embody altruism and mercy and imitate God.

Looking at the Vitruvian Man, it becomes clear the message that Leonardo was trying to deliver to our subconscious. By changing our position we can fill the infinite spaces of a circle or a square should we wish. He enlightened us with the knowledge that mankind can fill whatever shape it pleases, both geometrically and philosophically.

The ability to answer a mathematical and philosophical problem with a “simple” drawing is where one can truly appreciate the genius of Leonardo da Vinci.

This essay was heavily inspired by TED-Ed’s video, The Vitruvian Man of Math. I strongly recommend that anyone who found this interesting should also watch the video. Link below:

About the author: Ahad Khattak’s eccentric skill set ranges from drawing to lock-picking and he thoroughly believes that the light of hope is the bane of all logic and sense in a human being.


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